1. Field of the Invention
The present invention relates to flywheel energy storage systems, and more specifically, it relates to such systems employing electrostatic generator/motors.
2. Description of Related Art
Electrostatic generator/motors, as pioneered by Professor J. G. Trump, and, as described in the prior art, can be operated in either a generator or a motor mode (see, e.g., J. G. Trump, “Electrostatic Sources of Electric Power,” Electrical Engineering 525, June 1947). Such devices have application to flywheels for bulk energy storage and robust motors, among myriad commercial and defense uses. This invention describes improved component configurations, electronic drive elements and parametric operational modalities for these devices, resulting in embodiments capable of functioning under the application of higher drive voltages than in the prior art, as well as with relaxed design rules and device constraints.
Electrostatic (ES) generators, an example of which is described in the prior art by the present inventor (U.S. Pat. No. 7,834,513 B2), operate with high electric potentials between stationary plates (stators) and moving plates (rotors), with each plate comprised of an annular array of electrodes. In general, for such ES generators, the achievable power output is determined primarily by four factors: (1) The voltage between the stator and rotor electrodes; (2) The maximum value of the capacitance of the electrode system, as determined by the geometry and material properties of the ES device; (3) The ratio of the maximum and minimum capacitance of the electrode system, Cmax and Cmin, respectively, that comprises the ES device; and (4) The operating frequency of the ES generator, as determined by the rotation speed of the rotor and the azimuthal periodicity of the segmented electrodes. Of these four factors, the key metric, in terms of device capability, is the first item listed above, namely, the operating voltage, as applied to the ES device. This follows, since it is known that for ES generator and motors, the characteristic electrical power that governs the operation of the device, be it the power output in the case of ES generators, or, the input drive power, in the case of ES motors, varies as the square of the peak voltage appearing between the opposing set of electrodes. A secondary metric pertains to the fourth item listed above, namely, the operating frequency of the device. In general, the operating frequency is equal to the product of rotation rate of the rotor and the number of annular electrodes about the circumference of the same.
Given that the ES devices cited in the above-noted prior art employ a so-called “resonance effect” to enhance the performance of the device, the third item listed above is not as critical a parameter as it is for other prior art ES systems that do not incorporate such parametric enhancements. Hence, in the present case, lower values of the capacitor ratio, Cmax/Cmin, can now be of practical use, as opposed to devices in the absence of parametric enhancements, whereby such low capacitance ratios may otherwise have been insufficient to achieve a given maximum power output, all else being equal. This invention teaches device embodiments that involve novel electrode geometries, which, relative to the prior art, can enable the application of greater ES device voltage levels across the electrodes (recall Item 1 above), as well as extending the range of allowable operating frequencies (recall Item 4 above). An example where such improved ES generator/motor systems can prove useful is in its application to flywheels for bulk energy storage.
In general, electrostatic (ES) generator/motors involve the use of an assembly of rotating and stationary elements that together comprise a condenser (or, capacitor), the capacitance of which varies periodically with the motion of the rotating elements relative to the fixed elements. An example of the prior art is shown in FIG. 1A (top view) and in FIG. 1B (Section A-A′: side view). Turning now to FIG. 1A, a circular array of fan-like stationary elements, 100, is depicted. Below this stationary array of elements is a similar circular array of elements, which is allowed to rotate about a vertical axis, referred to as the “rotor.” FIG. 1B shows a cross-sectional side view of the overall ES structure, showing an embodiment consisting of a set of two rotors, 106, with each respective rotor also comprised of a circular array of fan-like elements. Each respective rotor plate 106 is bound on each circular surface by a respective pair of stationary arrays, of opposing, fan-like elements. In the dual-rotor example shown, there are two equivalent pairs of stators, arranged in a stacked configuration, with the central stator 104 common to both. One pair of stators is comprised of plates 100 and 104; and, the second pair of stators is comprised of plates 104 and 102, respectively. The rotor plates are allowed to rotate about an axis oriented orthogonal to the plane of the fixed plate(s), as shown in FIG. 1A.
As shown in FIG. 1B, the rotors, 106, are comprised of a set of annular fan-like elements, with each element having a thickness greater than the basic substrate of the rotor disc. In general, the thick fan-like sections elements of the rotor can consist of a metallic (conductive) material, a dielectric material or combinations thereof. Each pair of fixed fan-like elements, which comprises the opposing stationary plates, forms a capacitor of a fixed gap, g, in between which, each respective rotor rotates. As the moving discs revolve about its axis, the capacitance between each pair of opposing stationary plates will vary periodically, owing to differences in the effective gap dimension, g, and the properties of the rotor material, as each fan-like element of the rotor passes between each respective annular capacitor element in the array. Note that this basic configuration of FIGS. 1A and 1B can be classified as a planar geometry, since the effective capacitors are formed via the opposing planar surfaces of the stators and rotor.
In general, ES structures can be configured either as an electrostatic (ES) generator or as an electrostatic (ES) motor, dependent upon the details of an electrical circuit that includes this device. In the so-called “generator mode” of operation, rotation of the moving element results in the generation of an ac voltage arising from the basic equation for the voltage across a charged condenser when the capacitance varies with time, as indicated by Equation (1):
                              V          ⁡                      (            t            )                          =                              q                          C              ⁡                              (                t                )                                              ⁢                                          ⁢                      (            Volts            )                                              (        1        )            Here q (Coulombs) is the charge on the condenser and C(t) (Farads) is the time-varying value of the capacitance, the latter owing to the relative rotation of the rotor with respect to the fixed stators. If the capacitance varies periodically with time, then the ac output of the electrostatic generator will also be periodic, with an ac waveform that depends upon the geometry of the time-varying condenser and upon the charging circuitry that is employed.
The variable-capacity system described above is a “reciprocal” device, in that it is capable of functioning either as a generator or a motor, depending only upon the circuitry to which it is attached. As a generator, an example of which is an energy storage flywheel, the generator output is high-frequency alternating current, which can easily be converted to mains-frequency power. As an example, the high-frequency generator output can be first rectified to dc, with the resultant dc output driving an electronic inverter to produce a 60 Hz output, the latter suitable for commercially powered devices.
By reciprocity, operation of the system in the so-called “motor mode” requires a drive circuitry that generates a pulse-like waveform, which is synchronized with the rotation frequency and phase of the rotating elements.
In the electronic charging circuits such as those described in the prior art, dc power supplies are connected in series with charging inductors to the time-varying capacitors that form the ES generator. When these inductors are properly specified, an effective “parametric resonance” effect occurs, essentially coupling the LC-based charging frequency and the time-varying generator output, the latter being a function of the rotation rate and the number of fan-like annular elements in the array. This parametric effect resonantly increases the voltage gradient across the generator electrodes and enhances its power output and efficiency, far beyond that which can be achieved with the original resistive (instead of inductive) charging circuits such as those used in the pioneering work on ES generators by Trump.
FIG. 2 depicts an example of a prior art drive circuit, in which case a dual-balanced ES generator schematic diagram is shown. This circuit employs the parametric resonance effect noted in the prior art for enhanced device operation. The circuit has been shown by computer code simulation to enhance this parametric resonance effect. This approach enables the use of relatively low drive voltages, as well as relatively small capacitive ratios, Cmax/Cmin, to realize enhanced ES device performance over the prior art. In the circuit of FIG. 2 the parametric resonant effect is achieved by the proper choice of the value of the inductances in the circuit, based on the following: Starting at the point 254 in that circuit there is first an inductance (and its internal resistance), represented by 256 and 258. Next there are two time-varying condensers (260 and 360) connected in series. These condensers are followed by the inductance 356 and its internal resistance, with the circuit in question terminating at 354. This circuit represents a series-resonant electrical circuit, the resonant frequency of which will vary over a band of frequencies as the capacitors 260 and 360 vary synchronously between their maximum and minimum values. Strong parametric resonance occurs when that band of frequencies overlaps the frequency at which the capacities are varying. This latter frequency is determined by the product of the rotation speed of the system and the azimuthal number of periodic electrodes in the generator/motor (e.g., that number is 8 in FIG. 6A). If the rotation speed is constant fixed values can be used for inductances 256 and 356 of FIG. 2. If the rotation speed varies the inductance values must change accordingly. Such a change could be accomplished in several different ways, e.g. switching in or out additional series inductors, mechanically tuning the inductance (in the manner it was accomplished in early radio receivers), or by controlled saturation of the cores of iron-cored inductors. Fortunately, as analysis has shown, as long as there is an overlap between the operating frequency and the band of resonance the parametric resonance effect will be strong so that this inductance “tuning” need not be precise.
As an example, this circuit can be used to charge the ES device, as depicted in the prior art embodiment of FIG. 1A and FIG. 1B. In this case, each respective variable capacitor, 260 and 360, in FIG. 2 corresponds to a respective variable capacitor in the device shown in FIG. 1B, with each such variable capacitor formed by stationary plates 100 and 104, or by stationary plates 102 and 104, within which revolves a respective rotor plate 106.
Referring again to FIG. 2, each of the two balanced portions of the circuit is comprised of a time-varying capacitor, C(t). 260 [360], a fixed coupling capacitor, C, 268 [368], and a charging inductor, L, 256 [356], with each inductor possessing an internal resistance, represented by a resistor R, 258 [368], which together drives a load 400. By using the load to provide electrical coupling between the two circuit portions, the net effect is to lower the optimum load impedance, while at the same time, increasing the output power.
Each respective time-varying capacitor, C(t), consists of a pair of fixed stator assemblies, between which is an elongated rotor. Owing to the balanced nature of the circuit in the prior art example, the rotors operate at a virtual ground potential and, therefore, do not require a direct electrical connection to ground. Finally, the input to each portion of the balanced circuit is driven by a respective power supply at a voltage, V, 252 [352], each of which is of an opposing polarity.